The present invention relates to a taper cutting control unit for a wire-cut, electric discharge machine.
As is well-known in the art, a wire-cut, electric discharge machine has a wire electrode (hereinafter referred to simply as a wire) stretched in a taut condition between upper and lower guides and cuts a workpiece by a discharge which is produced between the wire and the workpiece. The workpiece is fixedly mounted on a table and shifted along a desired shape in the X and Y directions in response to commands from a numerical controller. In this instance, when the wire is stretched in a direction perpendicular to the table (or the workpiece), the workpiece is cut into a required profile whose top and bottom surfaces have the same shape. When the upper guide is adapted to be displaceable in the X and Y directions and is displaced in a direction perpendicular to the direction of travel of the workpiece so that the wire is held at an angle thereto for an angular cut, so-called taper cutting takes place by which the workpiece is cut into a required profile with top and bottom surfaces of different shapes.
FIG. 8 is a schematic diagram showing the general arrangement of such a four-axis control wire-cut, electric discharge machine, in which a workpiece WK is fixedly mounted on an X-Y table TB which is driven by motors MX and MY in the X and Y directions. On the other hand, a wire WR is paid out of a reel RL1 and wound onto a reel RL2 while being stretched between lower and upper guides DG and UG, and a voltage is applied from a contact electrode, not shown, to the wire, producing a discharge between it and the workpiece WR. The upper guide UG is provided on a column CM in a manner to be movable by motors MU and MV in the X and Y directions, respectively, and the motors MX, MY, MU and MV are driven by servo control circuits DVX, DVY, DVU and DVV of a numerical controller NC. When the contents of a command tape TP are read, processing for distributing pulses to each axis is performed by a distribution circuit DS. With such a wire-cut, electric discharge machine, taper cutting of the workpiece WK can be achieved by displacing the upper guide UG in the X and Y directions so that the wire WR is tilted with respect to the workpiece WK.
FIG. 9 is a diagram explanatory of such taper cutting. The wire WR is shown to be stretched between the upper and lower guides UG and DG at a predetermined angle to the workpiece WK. Now, assuming that a shape, into which the bottom surface PL of the workpiece WK is to be cut, is programmed (The shape into which the top surface QU of the workpiece WK is cut may also be programmed), and letting the angle of taper be represented by .theta..sub.0, the distance between the upper and lower guides UG and DG by H, and the distance between the lower guide DG and the bottom surface of the workpiece WK by h, the amounts of offset d.sub.1 and d.sub.2 of the lower and upper guides DG and UG from the bottom surface PL of the workpiece WK can be expressed as follows: EQU d.sub.1 =(h.multidot.tan .theta..sub.0)+d/2 (1) EQU d.sub.2 =(H.multidot.tan .theta..sub.0)-(h.multidot.tan .theta..sub.0)-d/2=(H.multidot.tan .theta..sub.0)-d.sub.1 ( 2)
where d is the width of a groove being cut in the workpiece.
Accordingly, when the movement of the upper guide UG around which the wire WR is directed is controlled as the workpiece is moved so that the amounts of offset d.sub.1 and d.sub.2 remain constant, the workpiece can be tapered at the angle .theta..sub.0, as depicted in FIG. 10. In FIG. 10, the broken line and the one-dot chain line indicate paths of the upper and lower guides UG and DG, respectively. During taper cutting, commands are usually issued on the programmed path on the bottom or top surface of the workpiece, the feed rate along the programmed path, the tapering angle .theta..sub.0, the afore-mentioned distances H and h, etc., thereby performing the cutting as instructed.
Incidentally, the wire-cut, electric discharge machine usually employs a circularly-bored die for taper cutting. FIG. 11 shows in section such circularly-bored dies which are utilized as the upper and lower guides UG and DG. In FIG. 11, reference character CH indicates a circular bore of the die, NSU a bottleneck portion of the upper guide UG, and NSD a bottleneck portion of the lower guide DG. The bottleneck portion of each guide is formed at an acute angle or slightly rounded. In the electric discharge machine using such circularly-bored dies as the upper and lower guides, the amount of travel of the upper guide UG relative to the workpiece is determined regarding the centers of the bottleneck portions NSU and NSD (indicated by black circles) as wire supporting points the positions of which determine the tapering angle, and the movement of the upper guide is controlled accordingly. That is, the amount of relative travel of the upper guide UG is calculated on the basis of the tapering angle .theta..sub.0 which is an angle between a straight line joining the both supporting points and the workpiece, the vertical distance H between both supporting points, and the distance h between the wire supporting point in the lower guide DG and the bottom surface of the workpiece, and the movement of the upper guide is controlled in accordance with the amount of its relative travel thus obtained.
In the case where the bottleneck portions NSU and NSD of the circularly-bored dies are formed acute or slightly rounded, since the wire has a predetermined diameter and a certain flexual rigidity, an increase in the tapering angle .theta..sub.0 causes the trajectory of the wire center to become as indicated by the broken line in FIG. 11, and so the wire no longer retains the angle .theta..sub.0. Furthermore, since the wire abruptly bends, its trajectory varies during running, resulting in a failure of high precision cutting.
In view of the above, the present inventor has previously proposed the following system which keeps the tapering angle as instructed and prevents the wire from shifting its position while in operation (see Japanese Pat. Pub. Disc. No. 28424/83, for example).
FIG. 12 is a sectional view for explaining wire guides for taper cutting by the electric discharge machine according to the above-said proposal. In FIG. 12, reference character WR identifies a wire, UG an upper guide, and DG a lower guide. A workpiece is disposed between the upper and lower guides UG and DG, though not shown. Those portions UGW, UGW' (the upper guide) and DGW, DGW' (the lower guide) of the upper and lower guides UG and DG along which the wire is guided on the side where the workpiece is disposed are each curved, in section, along an arc of a circle with a radius R, and those portions UGU and DGU of the guides which are on the side opposite from the workpiece are conically-sectioned. That is, both the oncoming side of the upper guide UG and the offrunning side of the lower guide DG are of circular (spherical) cross section with the radius R.sub.0. It is desirable that the value of the radius R.sub.0 be three times, preferably, five times or more larger than the wire diameter. With the inlet and outlet portions of the guides thus rounded in section along a circular arc with the radius R.sub.0, there is no longer posed the problem which arises from the bending of the wire WR.sub.0 as in the case of using the circularly-bored dies. In other words, the wire WR is smoothly guided through the dies and becomes less slack, so that it is possible to reduce the variations in the trajactory of the wire and the variations in the tapering angle owing to the rigidity of the wire.
With the guides of the structure depicted in FIG. 12, the essential wire supporting points shift to points A and A' respectively. The points A and A' are each the intersection of the vertical portion WRn of the wire WR with the center line of the taper cutting portion WRt. During programming the programmed path, the distances H and h, and the tapering angle .theta..sub.0 are commanded on the assumption that the wire is supported at points C and C'. Accordingly, during actual cutting the commanded or other data must be corrected on the basis of the tapering angle .theta..sub.0 ; this correction is effected in such a manner as follows:
Now, letting the diameter of the wire WR be represented by .phi., the distance .delta..sub.1 between the essential wire supporting points A, A' and the wire supporting points C, C' on the program is given by EQU .delta..sub.1 =(R.sub.0 +.phi./2).multidot.tan (.theta..sub.0 /2) (3)
and the essential wire supporting points A and A' approach each other in the vertical direction. Namely, the vertical distance Hc and the horizontal distance Dc between the essential supporting points A and A' are expressed by the following equations: EQU Hc=H-2(R.sub.0 +.phi./2).multidot.tan (.theta..sub.0 /2) (4) EQU Dc=Hc tan .theta..sub.0 ={H-2(R.sub.0 +.phi./2).multidot.tan (.theta..sub.0 /2)}.multidot.tan .theta..sub.0 ( 5)
Accordingly, the following methods can be employed for the correction:
[A] Noting the vertical distance between the supporting points, the distance Hc is obtained from Eq. (4), and taper cutting is controlled in accordance with the distance Hc. PA0 [B] Noting the horizontal distance between the supporting points, the distances of travel of the upper and lower guides are corrected on the basis of Eq. (5), without correcting the distance H. That is, the lower and upper guides DG and UG are moved to the left and to the right, respectively, by the following distance: EQU (R.sub.0 +.phi./2).multidot.tan (.theta..sub.0 /2).multidot.tan .theta..sub.0 ( 6)
However, the present inventor's experiments revealed that sufficient accuracy of taper cutting could not be obtained with such a correction alone.
As shown in FIG. 13, a 0.2 mm diameter wire was used as the wire WR, and a guide whose guideway had a 5 mm radius of curvature and had a minimum clearance of around 10 .mu.m between it and the wire was used as the guide GW. When taper cutting was actually performed for various tapering angles while applying a tensile force of 700 g to the wire WR, the actual tapering angles differed from commanded ones. The deviation .delta. of the supporting point of the wire WR, counted back from each actual tapering angle, was such as indicated by the solid line 1 in FIG. 14, from which it is seen that the above deviation differed relatively largely from the deviation .delta..sub.1 (indicated by the broken line 2 in FIG. 14) obtained from Eq. (3).